Some Further Results on Traveling Wave Solutions for the ZK-BBM(m,n)‎ Equations

Abstract EN

We investigate the traveling wave solutions for the ZK-BBM(m,n) equations ut+ux-aumx+bunxt+kunytx=0 by using bifurcation method of dynamical systems.

Firstly, for ZK-BBM(2, 2) equation, we obtain peakon wave, periodic peakon wave, and smooth periodic wave solutions and point out that the peakon wave is the limit form of the periodic peakon wave.

Secondly, for ZK-BBM(3, 2) equation, we obtain some elliptic function solutions which include periodic blow-up and periodic wave.

Furthermore, from the limit forms of the elliptic function solutions, we obtain some trigonometric and hyperbolic function solutions which include periodic blow-up, blow-up, and smooth solitary wave.

We also show that our work extends some previous results.